This invention relates to multiple discriminant analysis (MDA) and data integration of vibration in rotating machinery. As used herein xe2x80x9cdiscriminantxe2x80x9d is defined as xe2x80x9cA linear set of variables that will classify events or items for which the variables are measured with the smallest possible amount of misclassificationxe2x80x9dxe2x80x94Dictionary of Scientific and Technical Terms, McGraw and Hill, Fifth Edition.
Vibration analysis of rotating machinery to monitor life expectancy evolved following World War II, and has now been accepted as the most effective condition assessment and failure detection technique for rotating machinery. It is based on the principle that all rotating machines exhibit distinct operational and defect related vibration patterns that occur at rotational frequencies caused by forces, discontinuities, geometry placement and the physical condition of various machine elements. These vibration patterns change in energy and frequency content as the physical condition of the machine deteriorates. Measuring and interpreting the cause of the change enables those skilled in the art to detect problems early in the degradation process and initiate action to prevent machine failure, prevent production shutdown and potentially catastrophic failures. This technology has become the mainstay of modern predictive (PDM) and reliability centered maintenance (RCM) programs throughout the world. Various measurement techniques are hereinafter described, and the determinants derived are hereinafter described and discussed.
In spite of its technical effectiveness, the nature and complexity of vibration data and the process of extracting predictive failure data has added to the cost of its implementation and impeded its widespread commercial use. Highly skilled engineering level specialists, with extensive training, are often required for routine reviews and interpretations of data. The loss of one or two highly trained personnel can disrupt or cripple a major maintenance program.
Two of the most common techniques in general use for detection, measurement and analysis of vibrations in rotating machinery are Overall Measurement and Spectral Band Analysis. The overall measurement technique utilizes a piezoelectric crystal accelerometer to convert the mechanical vibration motion to a voltage proportional to the instantaneous acceleration mode vibration and monitors the root mean square (RMS) value of the broad frequency band displacement, acceleration or velocity signal. When the overall vibration level exceeds a predetermined threshold, a warning is initiated and inspection, repair, or machine shutdown action ensues.
This technique has the advantage of providing a single number, expressed in acceleration g units, in/sec velocity units or mil-inch displacement units, to indicate the machine condition. However, this technique has a weakness in that it often fails to detect subtle high frequency, low level bearing defects. High level energy from shaft imbalance and misalignment often dominates the overall signal causing it to be insensitive to low energy bearing problems. For this reason machinery bearing component failures often occur without warning, because this technique failed to provide adequate warning. The spectral band analysis technique, a more recent and improved technique employs a spectrum band analysis, where the vibration signal of defined bandwidth (upper and lower frequency content) is time sampled and converted into digital form. A Fast-Fourier Transform procedure is performed on the acquired data transforming it from the sampled time domain to the frequency domain in the form of frequency bands of varying amplitude. The level of each band indicates the frequency of the particular forcing function revealing its identity and its severity.
This format allows highly experienced maintenance personnel to directly observe the contributions of each problem source to the overall level at its own characteristic frequency. The individual frequencies, or spectral windows (placed around critical frequency bands) allow highly trained personnel to identify the source of a problem. For example, imbalance occurs at primary rotational frequency, misalignment at two or three times rotational frequency and the level of each component will identify the condition. Alarm levels are often preset for specific frequency bands. Levels above some predetermined levels indicate degradation. When the bands of interest include several selected narrow fast Fourier transfer bands, this technique is sometimes referred to as spectral windowing or enveloping.
This technique has the advantage of allowing the highly skilled maintenance practitioner (as used herein xe2x80x9cpractitionerxe2x80x9d refers to a person experienced in rotating machine maintenance) to observe both high and low level signals at high and low frequencies to detect both imbalance and bearing signals. This spectrum analysis technique is very effective when used by an experienced maintenance practitioner, but not very effective in the hands of most untrained maintenance personnel. The spectrum analyzers and other analysis devices required are complex and require highly specialized training. The spectral data generated by such techniques is voluminous and cumbersome to store track and interpret. For these reasons, use of spectral analysis has been limited to the use of large organizations, able to maintain highly skilled maintenance teams trained in vibration analysis, or to contract with outside consulting firms.
The nature of the data produced in spectral analysis technique poses technical problems as well. The data ranges in frequency from a few Hz to 30 kHz and signal levels ranging from microvolts to volts. This data presents special problems in terms of analog or digital data transmission and storage. More importantly, the raw data generated is not easily understood and useful to management personnel.
Accordingly the present invention provides a new and improved multiple discriminant vibration detection, analysis and data integration system and method that reduces an entire highly sophisticated vibration analysis process to a few uniquely derived discrete numbers in a predetermined range. These numbers quickly convey the useful information required by a non-technical user, or a skilled practitioner, in order to judge the reliability, dynamic condition, the expected life and/or the degradation state of a machine bearing or group of machines bearings. The derived numbers may be displayed in a variety of ways, but generally in a fashion where a first twenty percent of the range would indicate a normal or acceptable level, the middle forty percent of the range would indicate cautionary alert and the other forty percent would indicate alarm/action.
The invention further provides a new and improved system and method for providing a signal indicative of and visual indication of the life expectancy of the bearing based on the dynamic forces exerted on the bearing. This is provided as a xe2x80x9cstand alonexe2x80x9d signal exclusive of the present bearing degradation condition.
An object of this invention is to provide a new, improved and simplified method and system for determining the vibratory condition of a rotating machine with rolling element bearings.
Another object of this invention is to provide a new, improved and simplified method and system that utilizes detected vibration of a machine to assess the conditions in a rotating machine, both as to the present state of bearing degradation and as due to the composite dynamic forces acting on bearings that lead to a shortened life expectancy.
Another object of this invention is to provide a multiple discriminant analysis method and apparatus that may be easily used by non-technical management and unskilled or moderately skilled personnel.
A further object of this invention is to provide a method and system that uses system operational discriminants combined in a unique fashion to accurately signify present bearing condition and life expectancy.
Still further objects of this invention are to derive and provide a single factor that provides an indication of machine condition, which provides a technically comprehensive indication of dynamic conditions that contribute to shortened machine bearing life, and that provides a technically comprehensive indication of actual bearing state of degradation and a failure probability estimate.
Prior to summarizing the invention, it will be useful to discuss the discriminants detected from a raw acceleration signal and utilized in practice of the invention and systems embodying the invention.
Low Frequency Discriminant (LFD)
Imbalance, misalignment, belt resonance, warped shaft faults, and other such factors, that act to exert dynamic forces on the bearing element-race interfaces in a manner that reduces bearing life expectancy in rotating machinery, manifest themselves at frequencies at or near to the fundamental rotating frequency of the machine. For example: the dynamic force produced by a rotational imbalance is equal to the offset mass times the angular velocity squared divided by the radial offset.
Force=massxc3x97V2/r
Warped shafts, misaligned couplings contribute in the same fashion. All of these occur at frequencies close to the rotational frequency, and are the principal contributors to the dynamic force contribution. Most common industrial machines operate at rotational frequencies in the range below 7200 RPM (120 Hz). The LFD accepts the raw vibration signal, filters it to allow only inclusion of frequencies above 180 RPM (3 Hz]) and below 21,600 RPM (360 Hz), less than four times the 7200 RPM rotational speed. The upper corner frequency may vary for very low speed or very high-speed machines but should be roughly less then four times the shaft rotational frequency. For lower or higher speed machines the filter upper corner may be conveniently shifted up or down by means of a motor speed selection button. A low frequency filter allows these signals to pass and then converts the signal to a normalized RMS (root mean square) DC voltage such that normal vibration, on a scale of one to ten, is in the range of 1 to 2 volts, moderately excessive in the range of 2 to 6 volts and dangerously excessive is in the range of 6 to 10 volts. When this voltage is excessive it alerts the practitioner to a condition that will eventually reduce the expected life of the bearing. It also is clearly related to low frequency balance, alignment, belt resonance, eccentric shaft, or other such problem that can be determined by a skilled practitioner, all of which are referred to as xe2x80x98Dynamicxe2x80x99 forces. In accordance with one aspect of the invention the LFD is modified to provide a composite stand alone signal indicative of a Dynamic Force Factor (DFF) representative of the dynamic forces on the bearing
In accordance with the invention the next four discriminants are included in a formulaic approach to develop a Bearing Degradation Factor (BDF) as hereinafter explained.
High Frequency Discriminant (HFD)
When a rolling element bearing begins to degrade the bearing surfaces begin to develop microscopic surface defects. As the balls pass over the surface, they begin to generate highly scattered, high frequency impact energy, with periodicity roughly related to mathematical ball and race geometry, but with many generally unpredictable frequency components. Experience indicates that the bulk of the energy is contained in the high frequency region between 200 Hz and 10 kHz, and follows a somewhat predictable pattern during the failure process.
The HFD aggregates this high frequency data in the range of approximately four times the primary rotational frequency up to 10,000 Hz. In accordance with the invention the RMS value of the energy is converted to a DC voltage. The DC value of this voltage is generally proportional to energy of the vibration levels caused by rolling element bearing ball defects, inner and outer race defects, along with element rubs, and cage resonance. As an additional feature the raw input signal, prior to filtering, may be made available for more detailed spectral analysis by the practitioner.
Crest Factor Discriminant CFD)
Another and equally useful diagnostic technique for detecting early stages of bearing failure is called Crest Factor (CF) analysis. As part of the process of rolling element bearing deterioration, microscopic cracks develop on the rolling surface of the bearing, or the race. As the bearing rotates, these cracks contact the smooth opposing surfaces of the bearing and race. When the surfaces impact they generate very high amplitude, short duration, acceleration spikes, sometimes referred to as Dirac function spikes. Crest factor is the ratio of the time domain peak value of these transient impact accelerations to the overall RMS value of the selected vibration signal band. If the bearings were new, and the surfaces perfectly smooth, the vibration would be near sinusoidal and the crest factor would approach a sinusoidal value of peak to RMS ratio of 1.414. When defects develop, the Dirac peaks begin to increase in magnitude, but because they are of short duration they contribute very little energy to the RMS value, and the ratio of peak to RMS begins to increase. The CF value will rise, reaching values of four to seven or more. As the failure process continues the surface discontinuities will begin to wear, and the CF value will begin to decrease just prior to failure. Trending this CF value is a very good indicator of bearing condition and impending bearing failure, but requires specialized equipment and a highly skilled practitioner for effective implementation. The invention utilizes a DC value derived from the value of Crest Factor referred to as CFD.
CF is proportional to the expression pi=(xixe2x88x92xc3xc)/xc3xcxe2x80x83xe2x80x83(1)
Where: pi=crest factor,
xi=Instantaneous sampled value, and
xc3xc=RMS value of sampled waveform.
Typical variations in this variable ratio experienced in practice range from 1.5 to 7.0. In the practice of the invention a DC voltage is derived and scaled to provide the CFD.
Kurtosis Factor Discriminant (KFD)
The Kurtosis factor is a statistical measure of time waveforms peakedness. It is similar to Crest Factor in that it is also a ratio, but Kurtosis is the fourth moment of the peak to RMS ratio, and is therefore much more sensitive to changes in the peak value. It is often used as a very effective bearing defect diagnostic tool. In the invention a modified Kurtosis value KFD is derived from the sampled peak and the overall RMS value. Since it represents the fourth moment, the KFD discriminant is nonlinear, and is slightly more sensitive to early stages of bearing surface degradation than CFD. This is especially valuable when early detection of incipient bearing failure is critical. A typical example would be a cooling pump in a nuclear power plant.
KFD is proportional to m4=xcexa3(xixe2x88x92xc3xc)4/n between i=0 and i=nxe2x80x83xe2x80x83(2)
Where n is the number of samples, and
Where: m4=the mean Kurtosis value,
xi=instantaneous value of signal,
n=the number of samples, and
xc3xc=the mean value of 4th moment of samples.
A DC signal proportional to the value of the Kurtosis Factor is derived. In practice of the invention this DC signal is scaled to provide the discriminant KFD.
Envelope Demodulation Discriminant (EDD)
Another very useful detection and diagnostic technique, frequency envelope detection and demodulation, is widely used to detect early stages of bearing degradation. This technique also uses the high energy Dirac impulse phenomena described in the Crest Factor description, to extract still another form of defect information from the acceleration signal. The high energy Dirac spikes cause energy to be propagated throughout the frequency spectrum and initiate excitation of the vibration sensor crystal resonant frequency. This crystal frequency, often above 20/30 kHz, acts as a carrier. This carrier is modulated by the low frequency bearing ball spin and inner/outer race impacts. By band passing energy centered around the resonant frequency, detecting it and passing it through a low pass demodulation filter the low frequency envelope of the signal that contains information on the classic rolling element bearing defect frequencies, may be extracted. This band is again rectified and converted to a DC voltage proportional to the RMS magnitude of the demodulated defect energy. In addition, the real time, demodulated signal is made available and may be analyzed by the practitioner, to provide detailed spectral information on the nature of the defect if required. The demodulation information may be obtained by other means, for example by Hilbert transform techniques. See Shock and Vibration Handbook, by Cyril M. Harris, 3rd Edition, pages 13-45.
In accordance with the invention these discriminants provide the data for deriving three important factors, a Dynamic Force Factor (DFF), A Bearing Degradation Factor (BDF) and A Life Expectancy Factor (LEF).
Briefly stated, the invention, in one form thereof, provides a system for determining the various discriminants outlined above and combining signals representative of some of the discriminants in a simplified manner to determine the life expectancy, or remaining life of a rotating machine bearing, or the requirements for maintenance to extend and optimize the useful life of the machine, or to estimate the probability of machine bearing failure for some specified future operating period.
The vibrations of a rotating machine are detected by a piezoelectric accelerometer and applied to a plurality of channels where the discriminants identified above are determined. Four diagnostic routines or techniques, each designed to detect early degradation in rolling bearing elements, are performed on the detected acceleration signal to determine discriminants. The discriminants are converted to a voltage signal within a predetermined range as a measure of the particular factor.
The discriminants HFD, CFD, KFD and EDD are combined to display a value that signifies the condition of the machine bearings. The combining of the four discriminants stated above may be done by either an addition or a multiplication process and provides a Bearing Degradation Factor (BDF). The BDF is indicative of the instantaneous condition of the bearing.
A low frequency discriminant, LFD, as heretofore described is derived from the accelerometer signal that is indicative of the dynamic forces on the bearing. The LFD is essentially a dynamic force factor (DFF). This DFF signal may be weighted with other factors.
The BDF and DFF are combined in a weighted relationship to provide a life expectancy factor signal, LEF, which indicates the present condition of the bearing weighted by the dynamic loads thereon to give a composite indication of present bearing condition plus the effect of the dynamic loading of the bearing on its expected life and probability of failure.
The invention simplifies machine condition assessment and greatly improves the probability of accurate decision making on life extension, and bearing replacement by maintenance personnel.
The features of the invention that are believed to be novel are particularly pointed out and distinctly claimed in the concluding portion of this specification. The invention, however, together with further objects and advantages thereof may best be appreciated by reference to the following descriptions taken in conjunction with the drawings.